Argentina outclasses Mexico to advance
For the second consecutive match, though, there was controversy over a refereeing blunder.
Tevez was clearly offside when he headed in a chipped pass from Lionel Messi in the 26th minute at Soccer City. The referee awarded the goal after a lengthy consultation with his linesman as the pair was surrounded by angry players.
In the 33rd, Higuain rounded the goalkeeper to make it 2-0 after Ricardo Osorio, under no pressure, played the ball straight into his path. In the 52nd, Tevez scored one of the best goals of the tournament, running away from two defenders and sending in a powerful shot from 25 meters (yards).
"An important step," Tevez said. "We're in the quarterfinals and that's what matters."
Diego Maradona described the match as "tense" and accused the Mexicans of targeting Lionel Messi with overly-aggressive tackles - but said his players had deserved to advance.
"I want to congratulate them," he said. "Argentina was superior over 90 minutes. My players kept the ball well and passed it well."
Argentina will now face Germany in a rematch of the 1986 and 1990 World Cup finals. Germany also knocked the South Americans out in the quarterfinals in 2006.
"We have to rest and be ready for that game," Tevez said.
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After three convincing wins in the group stage, Argentina was favored going into Sunday's match, but Messi struggled to find space and Mexico came close to opening the scoring when Carlos Salcido hit the crossbar with a hard shot in the eighth minute.
Shortly after, Mexico teammate Andres Guardado burst through on a counterattack but his shot flew wide of the left post.
"The first couple of minutes were really difficult for us. We were not able to run the match," Tevez said. "That made life hard for us. After that, it only got better."
After the opening goal, the Argentines slowly took control of the game.
Tevez was proving a handful with his lively running, and Higuain - the leading scorer at the World Cup with four goals - should have added another but headed wide from point-blank range just before halftime.
As the players headed toward the tunnel, there were angry scenes as Mexican players had to be pulled away from Maradona and the match officials, furious at the circumstances surrounding the opening goal.
Earlier Sunday, Germany beat England 4-1 but that game was also mired in controversy after the referee ruled out a clear goal from England midfielder Frank Lampard with the score at 2-1.
In the second half, Mexico chased the game and at times Argentina had to resort to some frantic defending.
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Javier Hernandez pulled a goal back in the 71st minute after spinning off two defenders to fire a powerful shot into the top of the net.
Mexico coach Javier Aguirre refused to dwell on the opening goal by Tevez.
"I won't say too much about the refereeing," Aguirre said. "We lost our concentration after that offside goal. We were suddenly 2-0 behind, that was too much to catch up.
"We have a lot of young players, many are only 21," Aguirre said. "They will do even better in four years."
Messi, one of the outstanding players of the tournament, again failed to score, his best effort coming in injury time when his rasping shot was tipped over the bar.
Argentina: Sergio Romero, Martin Demichelis, Nicolas Burdisso, Gabriel Heinze, Angel Di Maria (Jonas Gutierrez, 79), Gonzalo Higuain, Lionel Messi, Carlos Tevez (Juan Sebastian Veron, 69), Javier Mascherano, Nicolas Otamendi, Maxi Rodriguez (Javier Pastore, 87).
Mexico: Oscar Perez, Francisco Rodriguez, Carlos Salcido, Rafael Marquez, Ricardo Osorio, Gerardo Torrado, Javier Hernandez, Efrain Juarez, Giovani Dos Santos, Andres Guardado (Guillermo Franco, 62), Adolfo Bautista (Pablo Barrera, 45).